Hamiltonian actions on 0-shifted cosymplectic groupoids

TL;DR

This paper develops a new theoretical framework for 0-shifted cosymplectic structures on differentiable stacks, including moment maps, reduction procedures, and convexity theorems, with applications to Lie groupoid morphisms.

Contribution

It introduces 0-shifted cosymplectic structures on stacks and establishes a comprehensive moment map theory with reduction and convexity results.

Findings

Established a reduction procedure for Hamiltonian cosymplectic actions.

Proved a version of the Kirwan convexity theorem in this context.

Provided examples of Morse-Bott Lie groupoid morphisms.

Abstract

We introduce the notion of 0-shifted cosymplectic structure on differentiable stacks and develop a corresponding moment map theory for Hamiltonian cosymplectic actions. We present a reduction procedure, establish a version of the Kirwan convexity theorem, and obtain examples of Morse-Bott Lie groupoid morphisms.